Embarassingly overdue, the slides of my talk on "Heavy Flavour and Quarkonia Production in 7 TeV pp Collisions", meant for the 2011 Les Houches meeting on "Recent Advances in QCD" to be held next week near Chamonix, France, are slowly coming together. Since these days I seem to be straggling my feet on the blog as well, I decided to kill two birds with one stone. So here you are going to get a short overview of recent measurements of b-quark production by CMS.

While providing the results for experts and beginners alike, I will try to make this discussion as simple as possible (but not simpler), something that lately I tend to forget. I do not like my blog posts to be too technical, but maybe I am getting old and my popularization powers are weakening. Let's see.

What it is about

The b quark is one of the six elementary matter particles that respond to the strong force, and bind together in hadrons. You know hadrons well: protons and neutrons are the prime examples, and they make over 99.9% of your own body mass by forming nuclei of hydrogen, oxygen, carbon, and the other stuff that your are build out of. But there are many, many hadrons that can be created out of quark-antiquark pairs or quark triplets. The former are called "mesons", the latter are called "baryons". But I won't be using this terminology any further, so I was just trying to annoy you with some useless information here.

So what is special about the b quark ? Well, it is the second heaviest one. It weighs like five whole protons all together. Physicists believe that there is a mystery to unveil here: the widely different masses of quarks is a puzzle and an exciting research topic. In truth, however, b quarks are interesting because by studying how they are created in energetic collisions we learn a lot about the force that binds quarks into hadrons. b quarks are special for other reasons, too; but I will not discuss these reasons here. Suffices to say that there are multi-billion-dollar projects designed with the sole aim of producing large numbers of b-quark hadrons: BaBar and Belle are past examples, but now there is also SuperB, a new facility that will one day see the light in the suburbs of Rome, Italy.

So let us stick to b production, and specifically, to how frequently and with what characteristics it occurs in the proton-proton collisions produced by the Large Hadron Collider, the powerful new CERN particle accelerator. While physicists could well guess the characteristics of b-quark production in the 7 TeV collisions that have taken place in the core of the CMS and ATLAS detectors from March to November last year, some details were not easy to predict. Producing b quarks

The proton normally does not contain b quarks. That is, it does, but only for extremely short periods of time: if you take a snapshot, only very rarely will you see a b-quark inside the proton. So it is hard to shake one out of a proton by smashing against it another proton. Much easier is to use the energy of a powerful head-on collision between a quark in one proton and an antiquark in the other: the energy converts into mass, so if there is at least 10 GeV of it -ten proton masses- the chance arises that a b-quark pair pops out.

The fact that 10 GeV is a very small fraction of the possible available energy from a LHC collision -it amounts to little over one per mille of the total collision energy- makes the theoretical calculation of b-production rates complicated, and thus a comparison of predictions with experimental results more interesting. The prediction is complicated for two reasons. Firsth, that in order to compute a predicted rate of production we need to know the probability to find a quark or a gluon inside the proton which carries a very small fraction of the total proton energy; and this is not well known. Second, the calculation at these small energy fractions involves the sum of large factors, which we do not know how to perform precisely.

The figure below shows a few "Feynman diagrams" that result in the production of b-quarks in proton-proton collisions. These diagrams describe how the initial-state quarks or gluons (straight or curly lines coming in from the left) collide, and how the energy materializes into the massive b-quarks. There are three different kinds of processes, at "leading order" (that is, in the most simple configurations capable of producing the reaction): direct production (the four top diagrams), flavour excitation (bottom right), and gluon splitting (bottom left). But I won't bore you with this detail here.

A reason to be happy for experimenters is that, despite the smallish amount of data produced by the LHC in 2010 (forty times more data is expected this year!), that is quite enough for some critical comparisons of experimental b-production rates with the predicted ones. This is because these rates are comparatively high! In 7 TeV collisions a b-quark is produced once in a few hundred cases, so in the two trillion collisions produced in the core of the detectors in 2010, one expects tens of billion b-quarks. The analysis reported below just used two thousandths of that data for a meaningful, precise result.

A CMS result: Open B Production Cross Section

One search for such processes was performed by identifying a muon. Muons -heavier copies of electrons- are rare in proton-proton collisions, but they are seen with extreme purity and efficiency by the CMS detector (guess what the M in CMS stands for). Muons are most of the times the result of the decay of a b-quark. By selecting events with muons, one automatically enriches the sample of b-quark decays. Then, by studying the relative momentum of the muon with respect to other particles traveling nearby (so-called jets of particles, produced in the materialization of stable bodies by the fragmentation of the original quarks or gluons created in a energetic collision) it is possible to understand how many of those muons really do come from b decay. This is shown in the graph on the right.

The variable called "Pt rel" is this relative momentum of the muon with respect to the jet. It is larger for b-produced muons (in red), because the b-quark is heavy, and in its decay it gives a larger kick to the muon than other processes do (in blue). A fit to the data distribution (black points) determiines the fraction of b-produced muons in the sample, and from that researchers are capable of calculating the total number of produced b-quarks. Then, this number is studied for different values of the kinematic characteristics of the muons -their transverse momentum (this time transverse refers to the proton-proton beam line, and not to the direction of the jet!), and their angle with respect to the beam. Actually, being such complex bastards, experimental physicists do not use the angle from the beam, which would be too simple to understand. They rather use the "muon pseudorapidity", which is the logarithm of the tangent of half the angle that the muon makes with the beam. Ah, change sign to that once you've computed it. There you go.

But worry not. Pseudorapidity may sound difficult, but it is just a number. The more the muon travels in the beam direction, the larger the number. So let us look at the rate of b-quark decays to muons as a function of muon transverse momentum and as a function of muon pseudorapidity, and check how it compares with theoretical predictions.

In the graph on the left you can see the CMS data points, with yellow shading highlighting the total uncertainty, compared with two different calculations. The data are presented as a function of muon transverse momentum here: this is a "differential cross section measurement", meaning that it shows the production rate for narrow intervals of the muon transverse momentum. As you can see, the data lies halfway between the MC&NLO predictions (a calculation performed by summing the contribution of many, many possible production mechanisms) and the Pythia predictions (a calculation produced by a computer program that simulates the various phases of the collision and b production processes).

In the other plot, shown below, you see the differential cross section as a function of muon rapidity. Here, again, you see the data halfway between the two predictions. Notably, though, the shape of the differential distribution agrees with the calculations.What do we learn from these measurements ? Well, from the comparisons we learn that there are important contributions that are not contained in the NLO calculation. The inclusion of "next-to-next-to-leading-order" diagrams (NNLO) in the calculation might, or might not fix the discrepancy. The fact that the disagreement is not only at low pT is an important input, too. But we also learn that the CMS experiment is up and running in important, detailed tests of quantum chromodynamics!

In the next post, if I find the time, I will describe another measurement of b production in CMS, one performed with a different technique - a full reconstruction of B+ mesons from their decay into J/psi K final states. Stay tuned if you are interested in this topic!

Comments

Sure, but I wanted to simplify the text and avoid discussing gluons so early on. By saying "matter particles" I exclude force carriers in the sentence. Unless you want to argue that gluons can also make up matter. It would not be wrong, strictly speaking, but confusing to a layman.

Tommaso, I don't quite get the purpose of this "parallel science for the laymen" that modifies important facts about science in order to be "less confusing". As far as I can see, even the laymen must ultimately be taught the real science, assuming something that they know, but they must be directed in the right direction.

To actively encourage them to nurture their belief that gluons don't interact by color, or that they're not a part of matter, is arguably pushing them in the opposite direction - in the left direction, also known as the wrong one. You may gain positive points as the "scientist of the people" who is always ready to defend the popular misconceptions - but you are not explaining them any science because meaningful explanations of science can de facto be *measured* by the number of wrong preconceptions that are replaced by the different, correct answers, or by the number of previously confusing insights that become "demystified" by the explanation.

If you're explaining things in a way that never runs into a collision course with the laymen's flawed preconception, then you're arguably explaining nothing important about science. You're just producing some irrelevant technicalities whose intimidating jargon will be used by the laymen to strengthen their incorrect beliefs about science.

we discussed this topic in the past already. We have a different view on it: you strive for accuracy, basically holding that science is hard and that there are no shortcuts, while I hold that some things may be conveyed if one sacrifices some accuracy -which most of the times is inessential.

It is no accident that the theorist among us is you, and the experimentalist among us is me.

About the details of your message above: I never said that gluons do not interact by colour. I did neglect them because of 100 laymen happening to read this post, I am conviced that 50 know that a proton is made up by three quarks, but only 20 know that the proton is more complex, and just one or two of them know that about half of a proton's energy is carried by gluons. My statements at the beginning of the post wanted to discuss b-quarks without mentioning inessential complications. But I suspect you concur with me and you are just being argumentative to keep exercised ;-)

Dear Tommaso, well, you can surely convey "something" if you don't care about the "accuracy" - which I would prefer to call "the truth" - but what you convey is often not true.

Do you really think that one may get the "message", whatever it is supposed to be, about the ways to produce B-quarks, while being kept in the belief that the gluons don't interact via color or that they're present inside nucleons? What do you think is more important: that the Yang-Mills fields have self-interactions, or that NNLO contributions may or may not fix a differential cross section with muon final states as a function of rapidity?

This is a preposterous question, isn't it? The self-interactions of the Yang-Mills fields are the first thing that one should know about them - and about QCD. It's a key to the secret what holds quarks together. Moreover, your own Feynman diagrams that you included have lots of vertices with gluon self-interactions, so you're not being consistent with your message. However, your very answer to this obvious question is upside down: you try to pretend that the NNLO gibberish is more important than the Yang-Mills gluon self-interactions.

Some NNLO corrections to a cross section with muon final states is approximately one million times less important than the things you decide to "hide". This is just not a communication of science. For the layman, you are just communicating impenetrable stuff that is completely wrong when it comes to the essential issues, and that unjustifiably tries to present one million times less important things as the key players - and you only do so to promote yourself.

This is what I call a sacrifice of integrity.

No, I really don't know what's the point of presenting any details about *any* strongly interacting processes if you decide to hide that gluons' self-interactions are essential to keep nucleons together, and for most of these processes as well (as your own diagrams show). Of course, the honest presentation is that your work is not relevant for anything that your 20 laymen may understand. You want to avoid this self-evident point, and arguably for egotistic reasons.

Enough Lubos. I can't, and I never wanted to, discuss the whole of particle theory in each and every post I put here. The main point in writing things in a comprehensible way is to get readers interested. The interested ones are ready to learn more, and will. I discussed the gluons and the strong force in a host of other posts.

And you did the right thing in pointing out the gluons. A post can never give a complete picture, and this is only achieved through the interaction with readers. The fact is, I have some experience with the presentation of HEP results to non-expert readers, and I have found out that it is much more important to drive home a result -the reader understand the main concept on which the post deals- than to be accurate in all one's side-statements. Unfortunately, accuracy makes the main goal harder to achieve: by being pedantic one scares or bores readers away, and gets many of the remaining ones confused.

Pythia is 40% higher than the data, but its prediction carries a large uncertainty as well. I would not say it is off by a few sigmas. The integrated result in the data is 1.32+-0.30 microbarns, while Pythia says 1.8 microbarns. No uncertainty was evaluated for it, but it is easy to imagine that it carries a uncertainty of at least 15% when PDF, b-quark mass, and scales are varied.

In the next post, if I find the time, I will describe another measurement of b production in CMS, one performed with a different technique - a full reconstruction of B+ mesons from their decay into J/psi K final states. Stay tuned if you are interested in this topic!

Great article Tommaso, I'm certainly hoping you find the time for the next post.